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Why prove (and not proves)?

Philosophicus, whether or not it prove to give the ultimate truth on the matters with which it deals, certainly deserves, by its breadth and scope and profundity, to be considered an important event in the philosophical world.

Bertrand Russell, Introduction to Ludwig Wittgenstein’s Tractatus Logico-Philosophicus , London, Kegan Paul, 1922

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    @user178049 That literature is dated 1922, so the vernacular is different. In today's time, the correct usage would be proves. Here is a link to the paper: writing.upenn.edu/library/Wittgenstein-Tractatus.pdf – Charles Aug 8 '17 at 12:40
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    Consider a simpler context featuring this (somewhat dated, as @Charles points out) subjunctive usage: Philosphy, whether or not it be useful in everyday life, is a core subject at many universities. The fact of the matter is subjunctive be there sounds somewhat laboured/pompous today, so learners should simply note that although it does still occur, it's best avoided. – FumbleFingers Aug 8 '17 at 13:24
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The subjunctive, in English has the same form as a bare infinitive. It can be used when the sentence is hypothetical in some way. The verb "prove" is here in its subjunctive mood. The use of the subjunctive has decreased in recent times, as noted in a comment:

Consider a simpler context featuring this (somewhat dated) subjunctive usage:

Philosphy, whether or not it be useful in everyday life, is a core subject at many universities.

The fact of the matter is subjunctive be there sounds somewhat laboured/pompous today, so learners should simply note that although it does still occur, it's best avoided. – Fumble Fingers

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